Solve for $x$ and $y$ using substitution. ${-3x+5y = 1}$ ${x = 5y-7}$
Answer: Since $x$ has already been solved for, substitute $5y-7$ for $x$ in the first equation. ${-3}{(5y-7)}{+ 5y = 1}$ Simplify and solve for $y$ $-15y+21 + 5y = 1$ $-10y+21 = 1$ $-10y+21{-21} = 1{-21}$ $-10y = -20$ $\dfrac{-10y}{{-10}} = \dfrac{-20}{{-10}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {x = 5y-7}\thinspace$ to find $x$ ${x = 5}{(2)}{ - 7}$ $x = 10 - 7$ ${x = 3}$ You can also plug ${y = 2}$ into $\thinspace {-3x+5y = 1}\thinspace$ and get the same answer for $x$ : ${-3x + 5}{(2)}{= 1}$ ${x = 3}$